Express this product in scientific notation: $(3.00\times 10^{3})\times (5.00\times 10^{1})$
Start by collecting like terms together. $= (3.00\times 5.00) \times (10^{3}\times 10^{1})$ When multiplying exponents with the same base, add the powers together. $= 15.0 \times 10^{3\,+\,1}$ $= 15.0 \times 10^{4}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $15.0$ is the same as $1.500 \times 10$ $ = {1.500 \times 10} \times 10^{4} $ $= 1.500\times 10^{5}$